Solution Posedness for a Class of Nonlinear Parabolic Equations with Nonlocal Term

摘要

Based on denoising, segmentation and restoration problems of image processing and combined with two-phase flow mathematical theory, this paper proposes a class of nonlinear parabolic equations with nonlocal term. By fixed point theorem, the existence of initial boundary value problem is gotten. And then this paper establishes solution uniqueness and stability about initial value $u_0$ and free term $f$.